Custom customer attribute: Magento 1.9

Question

I had a custom module Vendor_CustomerAccountExtended for customer modifications. Now I wanted to add there a custom attribute for customer(avatar). The problem is that I can create that attribute only if I delete that module from core_resource. What I have to do to create that attribute without this action? Before I start to modify that module I had only config.xml and AccountController. After that I added new lines of code in AccountController and the next files: etc/config.xml

<?xml version="1.0"?>
<config>
  <modules>
    <Vendor_CustomerAccountExtended>
      <version>1.0.1</version>
    </Vendor_CustomerAccountExtended>
  </modules>

  <global>
    <helpers>
        <vendor_customeraccountextended>
            <class>Vendor_CustomerAccountExtended_Helper</class>
        </vendor_customeraccountextended>
    </helpers>
    <resources>
        <vendor_customeraccountextended_setup>
            <setup>
                <module>Vendor_CustomerAccountExtended</module>
                <class>Mage_Customer_Model_Resource_Setup</class>
            </setup>
        </vendor_customeraccountextended_setup>
    </resources>
  </global>
 
  <frontend>
    <layout>
      <updates>
          <vendor_customeraccountextended>
              <file>vendor_customeraccountextended.xml</file>
          </vendor_customeraccountextended>
      </updates>
    </layout>
    <translate>
      <modules>
          <Vendor_CustomerAccountExtended>
              <files>
                  <default>Vendor_CustomerAccountExtended.csv</default>
              </files>
          </Vendor_CustomerAccountExtended>
      </modules>
    </translate>
    <routers>
      <customer>
        <args>
          <modules>
            <Vendor_CustomerAccountExtended before="Mage_Customer">Vendor_CustomerAccountExtended</Vendor_CustomerAccountExtended>
          </modules>
        </args>
      </customer>
    </routers>
  </frontend>
</config>

helper/Data.php

<?php
class Vendor_CustomerAccountExtended_Helper_Data extends Mage_Core_Helper_Abstract
{

}

sql/vendor_customeraccountextended_setup/upgrade-1.0.0-1.0.1.php

<?php
$this->addAttribute('customer', 'user_avatar', array(
    'type'      => 'varchar',
    'label'     => 'Avatar',
    'input'     => 'file',
    'position'  => 10,
    'required'  => false,//or true
    'is_system' => 0,
));
$attribute = Mage::getSingleton('eav/config')->getAttribute('customer', 'user_avatar');
$attribute->setData('used_in_forms', array(
    'adminhtml_customer',
    'checkout_register',
    'customer_account_create',
    'customer_account_edit',
));
$attribute->setData('is_user_defined', 0);
$attribute->save();